TANGENT: A Novel, “Surprise-me”, Recommendation
Algorithm
Kensuke Onuma
Hanghang Tong
Christos Faloutsos
Sony Corporation
1-7-1 Konan, Minato-ku
Tokyo, Japan
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA USA
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA USA
Kensuke.Oonuma@
jp.sony.com
[email protected]
[email protected]
ABSTRACT
Most of recommender systems try to find items that are most relevant to the older choices of a given user. Here we focus on the
“surprise me” query: A user may be bored with his/her usual genre
of items (e.g., books, movies, hobbies), and may want a recommendation that is related, but off the beaten path, possibly leading to a
new genre of books/movies/hobbies.
How would we define, as well as automate, this seemingly selfcontradicting request? We introduce TANGENT, a novel recommendation algorithm to solve this problem. The main idea behind
TANGENT is to envision the problem as node selection on a graph,
giving high scores to nodes that are well connected to the older
choices, and at the same time well connected to unrelated choices.
The method is carefully designed to be (a) parameter-free (b) effective and (c) fast. We illustrate the benefits of TANGENT with
experiments on both synthetic and real data sets. We show that
TANGENT makes reasonable, yet surprising, horizon-broadening
recommendations. Moreover, it is fast and scalable, since it can
easily use existing fast algorithms on graph node proximity.
mender systems; whereas, graph-based algorithms have been attracting great interest among researchers recently.
Most of the recommendation algorithms focus on the precision
in the proximity to user preferences. However, this strategy tends
to suggest items only on the center of user preferences and thus
narrows down the users’ horizons. According to the research about
the quality of recommender systems [20], broadening users’ horizons is one of important qualities for recommender systems. Such
systems provide a win-win situation: users may find more interesting items, and e-commerce enterprises increase their sales and their
user satisfaction.
Categories and Subject Descriptors
H.2.8 [Database Management]: Database applications—Data mining; H.3.3 [Information Storage and Retrieval]: Information search
and retrieval—Clustering, search process
General Terms
Algorithms, Experimentation
1.
INTRODUCTION
Recommender systems are vital for e-commerce sites, with most
striking examples being Amazon, Netflix, Pandora, Strands, etc.
Recommender systems are doubly useful: On one hand, they help
users filter through enormous numbers of available items, and focus on the few ones that match their preferences; on the other
hand, recommender systems help enterprises increase their sales
(e.g. movies, books, songs), on the long tail. Numerous algorithms for collaborative filtering [28] have been studied for recom-
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page. To copy otherwise, to
republish, to post on servers or to redistribute to lists, requires prior specific
permission and/or a fee.
KDD’09, June 28–July 1, 2009, Paris, France.
Copyright 2009 ACM 978-1-60558-495-9/09/06 ...$5.00.
Figure 1: The difference between conventional recommendation algorithms and TANGENT. Square nodes represent users
and circular nodes denote movies. Users are connected to
movies which they like. Black nodes are a target user and
his/her favorite movies.
In order to solve this seemingly self-contradicting problem, we
proposed TANGENT, a recommendation algorithm that takes into
account the connectivity to other groups in order to broaden users’
horizons. It is based on the graph mining technique of computing similarity between nodes and can be applied to any dataset that
can be represented as a graph. Figure 1 illustrates the difference
of results between conventional recommendation algorithms and
TANGENT. We assume that this synthetic bipartite graph records
rating information by users to movies. There are two groups in
this graph; fans for comedy movies and those for horror movies. If
“user A” rates two movies in the comedy group as favorite movies,
conventional recommendation algorithms would suggest movies in
the same group. In contrast, our proposed TANGENT method suggests a movie between two groups, to “surprise” the user and to
gently broaden his/her horizons.
The rest of the paper is organized as follows: we first review the
related work in Section 2; the proposed algorithm is presented in
Section 3; the experimental results are presented in Section 4; and
we conclude the paper in Section 5.
2.
RELATED WORK
In this section, we briefly review related work, which can be
categorized into three parts: graph mining, recommender system
and ranking and proximity on graphs.
Graph Mining. The main idea behind TANGENT is to envision
the problem as node selection on a graph. Graph mining itself is
a hot research topic in the recent years. For static graphs, representative work includes pattern and law mining [1, 6, 22], frequent
substructure discovery [34, 14], collective classification [4], fraud
and anomaly detection [21, 24], community mining and graph partition [11, 12, 16, 19], etc. More recently, there has been an increasing interest in mining time-evolving graphs, such as densification
laws and shrinking diameters [18], community evolution and dynamic [2], etc.
Recommender System. To our knowledge, there is little work
in recommender systems which focuses on broadening users’ interest. The work of Kamahara et al. [15], who explore methods for
locating unexpected items from similar clusters to user’s cluster, is
close to our problem. However, parameters such as the number of
clusters and thresholds, which are required in [15], are not easy
to be tuned. McNee et al. [20] raise a question about the current
accuracy metrics and propose some aspects which should give to
evaluation of recommender system.
Recommender systems have been attracting considerable research
interest, with recent emphasis on graph-based such systems. Fouss
et al. propose in [9] to apply Euclidean commute time distance,
which is one of random-walk-based methods of computing similarities between nodes, to a collaborative recommendation. Wang
et al. [33] apply a node similarity algorithm to item-based recommendation. Bell et al. [3] propose a low rank matrix approximation
method for collaborative filtering and successfully apply it to the
NetFlix competition. Although different in the specific methods,
the basic idea behind all these methods is to find items that are
most relevant to the older choices of the given user.
Ranking and Proximity on Graphs. In the literature, there
are several methods for calculating relevance (a.k.a similarity) between nodes on graphs. Because the shortest path, which is a conventional property for representing relevance, fails to capture the
multiple faceted relationship between nodes on the graph, random
walk based techniques such as PageRank [25], personalized PagerRank [13], Random walk with restart [30, 32], Euclidean commute
time distance [9], escape probability [8, 17] have been widely applied recently. In this paper, we use random walk with restart; however, the idea behind TANGENT can be naturally extended to other
proximity measurement.
The upcoming “bridging score” in our proposed TANGENT is
also related to the node betweenness: The betweenness of a node
is high if the node lies on the paths between many other pairs of
nodes. Intuitively, such a node is a good “bridge”, and deleting
such a node may often disconnect the graph. Freeman [10] proposes a method for computing betweenness based on shortest paths,
and Brandes [5] studies a fast algorithm for computing centrality.
On the other hand, Newman [23] also proposes fast algorithms to
compute, by using a random walk on the graph.
The degree of connectivity in a graph (which is the core idea behind the bridging score in the proposed TANGENT) is also related
to the degree of anomaly in a graph because the nodes with considerable links to various groups are considered to be anomalies. Sun
et al. [30] introduce the normality score of a node as a measure of
how homogeneous (i.e., interconnected) its neighbors are.
Although potentially useful for TANGENT, none of these methods have been used in a recommender system.
3. THE TANGENT ALGORITHM
In this section, we describe details of the proposed TANGENT
algorithm.
3.1 Notations and Problem Definitions
Symbol
A = (aij )
Ã
b = (bi )
D = (dij )
E
ei
G
k
li
m
n
r̂Si
Q = (qi )
R
Ri
ri = (ri,j )
rQ = (rQ,j )
Si = {si,j }
tQ = (tQ,i )
V
wij
Description
the weighted adjacency matrix
the normalized matrix of A
the
Pvector of bridging score
dii = j aij and dij = 0 for i = j
the set of edges in G
n × 1 unit vector (all zero except one at row i)
the weighted, undirected graph
the number of query nodes
the number of edges connected to node i
the number of edges in G
the number of nodes in G
the average of all non-diagonal elements in Ri
the set of query nodes (1 ≤ i ≤ k)
the matrix of relevance score
the similarity matrix among nodes ∈ Si
the vector of relevance score to node i
the vector of relevance score to query nodes Q
the set of nodes which have links to node i
the vector of TANGENT score
the set of nodes in G
weight on each in (i, j) ∈ E
Table 1: Symbols
Table 1 gives the main symbols used in this paper. We assume
that we are given a weighted, undirected graph G = (V, E), where
V denotes the set of nodes and E represents the set of edges. n is
the number of nodes and m is the number of edges. This graph has
weights wij > 0((i, j) ∈ E) on the edges. Since the graph is undirected, the weights are symmetric (i.e. wij = wji ). The weight wij
should indicate the strength of the relation between node i and node
j. Let A = (aij )i,j∈V be the adjacency matrix of the graph with
aij = wij if (i, j) ∈ E and aij = 0 otherwise. A set of query
nodes can be represented by Q = (qi )1≤i≤k .
Let us consider a movie-rating data set. Basically this database
consists of three kinds of information; demographic information
about the users, information about the movies, and information
about rating which users assigned to movies they have watched.
Each user and movie corresponds to a node, and each user is connected to the corresponding movies by edges weighted according
to the degree of rating. This graph expresses the relation between
users and movies (a user-movie graph), and is constructed as a bipartite graph. In this graph, nodes can be divided into two disjoint
sets such as V = {V1 , V2 }. A query node corresponds to a user
to whom the recommender system want to give recommendations
(i.e. k = 1).
Now we define the TANGENT problem as follows:
P ROBLEM 1 (TANGENT).
Given: an edge-weighted undirected graph G with adjacency matrix A, the set of query nodes Q = (qi )1≤i≤k .
Find: a node that (1) is close enough to Q, and (2) has high potential to reach other nodes.
3.2 Alternatives and Subtle Problems
Here we quickly review algorithms for computing ranking and
proximity on graphs and introduce alternatives we have explored
to solve our problem but find to be inapplicable because of subtle
problems.
Relevance Score. As described in Section 2, there are numerous methods to measure similarity ri,j between a pair of nodes (i,
j): escape probability, random walk with restarts, electricity-based
[26], maximum flow, to name a few. Although most of them give
reasonable scores, none of them takes into account the connectivity to other groups. Therefore, they can fulfill only the first of our
requirements.
It is an additional, subtle question on how to measure group proximities, that is, how close is node i to the set P
of query nodes Q.
Averaging, or just adding the individual scores q∈Q rq,i is a reasonable, but not necessarily the best choice. Another choice would
be to take the maximum such score, roughly corresponding to an
‘OR’: a node gets high score if it is close to at least one of the query
nodes. The list continues: the product is also a reasonable choice
(corresponding to an ‘AND’), and the CePS algorithm [31] gives
additional, more sophisticated choices.
Negation of Relevance Score. One of our first approaches to
solve the “surprise me” query problem was to consider negation.
Specifically: “Find nodes close to one query node, but far away
from all other query nodes.” That is, we want a candidate node v
that has high proximity to only one of the query nodes, and as far
as possible from the rest. We assume that a relevance score corresponds to probability, such as steady-state probability [32]. Since
multiplication of scores corresponds to conjunction, 1-complement
would correspond to negation, and thus the score of a node v should
be
Y
(1 − rqi ,v )}
(1)
negation(v , Q) = max {rqj ,v ×
1≤j≤k
i=j
However, although this equation has solid foundation in logic,
when used on large, real graphs, it gives almost the same arithmetic scores as max1≤j≤k (rqj ,v ). This is because most proximity/relevance scores are extremely low ( 10−2 ) and thus the product of the (1 − rqi ,v ) terms is practically equal to 1.
Entropy. Among the methods we tried but eventually did not
work, is an entropy-based idea, inspired by maximum marginal
gains: a candidate node v would be good, if it would make maximum difference in the existing distribution of proximities. This
would mean that it opens horizons. That is, let rQ,i be the score of
node i wrt Q; let r̀Q,i be the score if we add node v to the query
set Q. We want the node v that maximize
P the difference of the entropy
(i.e.,
H(r̀
)
−
H(r
)
=
−
Q,i
Q,i
i∈V {r̀Q,i × log(r̀Q,i )} +
P
i∈V {rQ,i × log(rQ,i )}.
However, despite the fact that maximum marginal gain should
lead to “surprising” choices, they are too far away from query nodes
because they are the best choices to make uniform distribution of
proximities, which maximize the entropy.
Our main point of this detour is that, despite the wealth of ideas
on node proximity, there are subtle issues that need to be carefully
thought out.
scores calculated at the first part and also prevents the last merging
part from being complicated.
The rest of this section describes details of each part.
3.4 Relevance Score (RS)
First we would like to compute the relevance score of a single
node j, for a single query node qi . There are several methods for
computing the relevance score between nodes, as described in Section 2. Although we can use any algorithm to compute relevance
score, we propose to use random walk with restart [30, 32] in this
paper.
According to [30, 32], the relevance score rqi is computed by
the following formula:
rqi
= cÃT rqi + (1 − c)eqi
= cÃrqi + (1 − c)eqi
(2)
where à is the normalized adjacency matrix of A by normalized
graph Laplacian (Ã = D−1/2 AD−1/2 , where D is the degree
matrix of A.) and (1 − c) denotes the fly-out probability.1 Note
that A is symmetric because aij = wij = wji = aji . rqi is
determined by
rqi
= (1 − c)(I − cÃ)−1eqi
= R · eqi
(3)
from the derivation of equation (2).
One of solutions to obtain rqi from equation (2) is the iterative
method, iterating equation (2) until it convergences; however, we
propose to pre-compute R because we can obtain the solution of
rqi for all nodes from equation (3) with less online computation
costs. Details are described in subsection 3.7. Note that it can be
proved by equation (3) that
R = [r1r2 ...rn ]
(4)
If there are multiple query nodes, we compute a relevance score
from all query nodes by taking Boolean ’OR’ of relevance scores
to query nodes by
rQ,j = 1 −
k
Y
(1 − rqi ,j )
(5)
i=1
3.5 Bridging Score (BRS)
Bridging score means the degree of connectivity to other groups
on a graph. Although betweenness [5, 10, 23] might be one of
the criteria for it, their algorithms are completely different and also
require a considerable computation costs. Or, we might use the
sum of weight of links connected to the corresponding node as an
3.3 Framework of TANGENT Algorithm
index considering that the popular items might have potential to
In this subsection, we illustrate the framework of our proposed
bridge groups. However, popularity does not always correspond to
algorithm.
The function of TANGENT can be described as tQ = tangent (A, Q) the connectivity to other groups.
We proposed to apply an anomaly detection algorithm on a biwhere tQ = (tQ,i )i∈V is a vector of degree of recommendation, to
partite graph [30], which is based on the relevance scores described
which we refer as TANGENT score in this paper. We would like
above, to any kinds of graph. The level of connectivity of a node
to have a recommendation algorithm for suggesting items which
on a graph is related to the level of anomaly on a graph because the
are not only relevant to user preferences but also have large connodes with considerable links to various, otherwise disjoint groups
nectivity to other groups. In order to fulfill these requirements,
are considered to be anomalies. Moreover, the merit of using the
TANGENT algorithm consists of three parts as follows.
same algorithm is that we can share the result of computing rele1. Calculate relevance score (RS) of each node : rQ .
vance scores. From equation (4), R expresses the relevance scores
2. Calculate bridging score (BRS) of each node : b.
from each node to each node and we can re-use R for computing the
3. Compute the TANGENT score (tQ ) by somehow merging
bridging score. This is important, because TANGENT only needs a
two criteria above.
1
c is the only parameter in the proposed TANGENT. However, we
Moreover, the algorithm for computing bridging score is defind that the recommendation result of TANGENT is insensitive to
c. Therefore, we fix c to be 0.5 throughout this paper.
signed to use relevance score, which re-uses the result of relevance
few relevance scores, and thus it can exploit any of the fast, known
algorithms, to compute such scores, like B LIN/BB LIN [32] and
variants.
Algorithm 1 Bridging Score (BRS) Computation Algorithm
1: Given: Adjacency matrix A
2: for i = 1 to n do
3: Pick up node i and let Si = {si,j |0 ≤ j ≤ li } be a set of nodes
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
Figure 2: Illustration of the procedure of computing bridging
score.
Figure 2 presents the procedure of computing bridging score. Let
li be the number of edges connected to node i. Given a node i, we
first find the set of nodes to which i links: Si = {si,j |0 ≤ j ≤
li }. Then we compute the relevance scores between any pair of
elements in Si and construct a li × li similarity matrix Ri . After
that, we take the mean of all non-diagonal elements in Ri and get
bi by inverting it. If node i is connected by only one edge or it has
no connection, we define its bridging score as bi = 0, which means
that it is not taken into account as a candidate of recommendation.
Figure 3 shows the intuition of computing bridging score. If i
is connected to one group, then the relevance scores between any
pair of elements in Si should be high and as a consequence, bi
become small. On the other hand, if i has links to several groups,
the relevance scores between different groups have small numbers
and we get large bi .
Figure 3: The intuition of computing bridging score.
Algorithm 1 summarizes the algorithm of computing bridging
score. Note that b is independent from query nodes Q. Therefore,
it can be pre-computed.
3.6 TANGENT Score
There are several ways to combine the above two criteria. However, again, reasonable-looking choices may suffer from subtle issues. We discuss them first, and then give our proposed combination method.
Reasonable-Looking, but Unsuccessful Choices. One natural method
to try is linear combination: i.e. tQ,j = rQ,j + α × bj (let α be
the coefficient). However, (a) the two values typically differ by orders of magnitude, and the larger, bj , typically overshadows rQ,j ,
(b) the method is not parameter-free anymore: somebody, somehow, needs to determine a good value of α, which may need to be
changed as the graph grows.
Our second approach, also reasonable-looking, but also unsuccessful, is to use skyline queries. Since we do not know how much
which have links to i;
if (li = 0) OR (li = 1) then
bi = 0;
else
Compute the relevance score vector rsi,1 rsi,2 , ..., rsi,li from
each Si = s1 , ..., sli ;
Construct li × li matrix Ri = [
rsi,1 rsi,2 ...
rsi,li ];
Take the average of all non-diagonal elements in Ri and obtain
r̂Si ;
Divide one by r̂Si , and obtain bi = 1/r̂Si ;
end if
end for
return a vector of bridging scores b.
weight to give to each of the two criteria (relevance vs. bridgeness), we could try multi-objective optimization, which leads to
skyline queries [27]: Given a set of multidimensional points D, a
skyline query finds the skyline points from D, that is, those points
that are not totally dominated by any other point in D. For example, if a point p is on the skyline, there is no data point p in D
such that p is larger than p for the values in all dimensions. The
example of a skyline query is shown in Figure 4. Movie A, B and
C are on the skyline and there are no other nodes which have larger
relevance score as well as larger bridging score than points on the
skyline.
However, using skyline queries for our setting suffers from the
following subtle drawbacks: (1) it cannot keep the balance between
the two criteria; for instance, a skyline query extracts a node which
has the highest relevance score even if it has zero bridging score
(see Movie C in Figure 4) and vice versa, (2) the skyline also neglects second-best candidates. (In Figure 4, movie Z dominates
everything else, and thus we would only return that movie, even if
Movie Y is also a good candidate.)
Figure 4: The examples of a skyline query.
Proposed Combination Method. A reasonable and well performing method is multiplication: i.e. tQ,j = rQ,j × bj = rQ,j /r̂Si . It
can be seen from the equation above that tQ,j represents the ratio
between relevance score to query nodes and relevance score among
neighbors. Notice that all our proposed choices are parameter-free,
making TANGENT parameter-free, as we required.
3.7 Scalability
We want TANGENT to be parameter-free2 , effective and fast.
The first goal is achieved as we showed. The second goal is discussed in details later. Here we illustrate the achievement speed.
Specifically, we discuss the scalability of the TANGENT algorithm
by discussing each of the first two parts. The third part, merging, is O(n) since it needs just a multiplication for each of the
n − q = O(n) candidate nodes.
Computing Relevance Score. Although computing R in a straightforward way requires cubic computation cost to the number of node,
2
As mentioned before, the only parameter c in TANGENT has little
influence on the result and is fixed to be 0.5 throughout this paper.
there is a fast algorithm to get good approximate solution of random walk with restart proposed by [32]. Once we pre-compute
R, online computation cost for computing relevance score for each
node is only matrix-vector multiplication shown in equation (3).
Computing Bridging Score. It can be seen in Algorithm 1 that,
R, which is pre-computed for computing relevance score, can be
re-used in computing bridging score. Therefore, the online computation of this algorithm takes time O(n). Moreover, in case of
a user-movie bipartite graph, we do not need to compute bridging
scores of user nodes for recommendation; therefore, the computation cost can be reduced to the number of movies. If faster online
computation is required, we can pre-compute it since the bridging
score is independent of the query.
4.
EXPERIMENTAL RESULTS
In this section, we evaluate the effectiveness of TANGENT. Since
the objective of TANGENT is to find the neighbors of user preference with large connectivity to other groups, not to improve the
accuracy of recommendation, conventional evaluation metrics such
as degree of agreement[9], a percentile score[9], a recall score[9],
mean absolute error[29], MSE[33], and NMSE[33] do not work on
the evaluation of effectiveness for TANGENT algorithm, neither
does questionnaires asking whether the recommendation made by
the algorithm is satisfactory or not. Therefore, we evaluate its potential on a number of synthetic graphs as well as on real data sets.
For both synthetic and real data set, we present (1) the case studies which show that TANGENT gives reasonable results; and (2)
systematic comparisons with conventional recommendation algorithms (i.e., by relevance score) which show that TANGENT tends
to return more surprising results. Let ntan and nrel be the surprising nodes in the returned recommendation list by TANGENT and
by conventional recommendation algorithms, respectively. We de−nrel
fine the “Surprising Gain” as ntan
. A big “Surprising Gain”
nrel
means that TANGENT returns more surprising results compared
with conventional recommendation algorithms.
Figure 5: Relevance score, bridging score, and TANGENT
score of each node on synthetic unipartite graphs. A query
node is represented by a black node.
described in Figure 1, square nodes represent users, circular nodes
denote movies, and edges correspond to ratings by users. Graph
1 and Graph 2 in Figure 6 have almost same structure, except that
user 1 and movie 24 are linked with each other in Graph 2.
4.1 Evaluations on Synthetic Data Sets
Case Studies on Unipartite Graphs. We start off by presenting
unipartite graphs, which have several groups in them and are connected by nodes. In the experiment, we compare the ranked lists
based on relevance score, bridging score, and TANGENT score.
The graph on the left side of Figure 5 has two groups; nodes 1 - 4
in Group 1 and nodes 6 - 9 in Group 2, which are connected through
node 5, and we run a query for node 1. Node 2 gets the highest relevance score among nodes except the query node, followed by nodes
3 and 4. This result would be same as what conventional recommendation algorithm would give. On the other hand, comparing
bridging scores, we find that node 5 gets the highest score, because
the neighbors of node 5 (nodes 3, 4, 6 and 7) are separated in half
into two groups and, as a consequence, the average of relevance
scores among them becomes small. Notice that nodes 7, 3 and 4
also get relatively high bridging scores. As a result, nodes 3 and 4
are ranked as No. 1 in terms of TANGENT score, as reflects our intuition that these nodes are close enough to the query node as well
as getting close to Group 2.
The graph on the right side of Figure 5 has four groups and two
query nodes in different groups. In this case, both node 3 and node
12 are considered as bridging nodes; however node 3 should be
considered as a better bridging node than node 12 because node 3
leads to Group 2, which is larger than Group 3. As we can see,
TANGENT algorithm gives a result which follows our intuition.
Case Studies on Bipartite Graphs. We next evaluate the effectiveness of TANGENT algorithm on synthetic bipartite graphs.
Figure 6 illustrates the structure of graphs and the results. As we
Figure 6: No.1-ranked movie for several query nodes on synthetic bipartite graph. Dark nodes are query nodes.
We can derive some fascinating observations from this figure as
follows: (1) In Graph 1, movie 16 gets the highest TANGENT
score for user 1. This result completely agrees with our motivation described in Figure 1. (2) In Graph 1, TANGENT algorithm
concludes movie 20 to be the best recommendation for user 5, not
movie 16. It is a reasonable result because movie 20 is watched
by three groups; while movie 16 is watched by two groups. (3)
In Graph 2, TANGENT algorithm still suggest movie 16 for user
1, not movie 20. Recommender system does not have to be sensitive to outliers. In this case, user 1’s preference still lies on the
group where s/he involves and TANGENT takes it into account.
This result indicates that TANGENT is robust to exceptionally favorite movie. (4) In Graph 2, movie 24 gets the highest TANGENT
score for user 12, despite the fact that movie 20 is recommended in
Graph 1. Comparing movie 20 and movie 24, we find that movie 24
has higher relevance score than movie 20, and also movie 24 has
connectivity to another group in Graph 2. This structural change
causes the difference of the recommendation results.
Comparison with Relevance Score. Finally, we systematically
compare the proposed TANGENT with conventional recommendation algorithms. The goal of TANGENT is to provide some
“surprising” recommendations, i.e., to find the neighbors of user
preference with large connectivity to other groups. Formally, for a
given query node q, we say the recommended node i is “surpris-
gorithm still recommends diverse genres of movies; not only horror
but also thriller, crime, and drama.
0.35
TANGENT
Rel
0.25
2.5
TANGENT
Rel
0.2
2
0.15
0.1
0.05
0
1
2
3
4
recommendation list length
5
Figure 7: Comparison of TANGENT and conventional recommendation algorithms on synthetic graphs. Higher is better.
ing” if (1) nodes i and q belong to the same group, but the node i
has some links to other groups; or (2) nodes i and q belong to the
different groups, but the node i has some links to the same group
as the query node q. For example, in the left graph of Figure 5,
nodes 3-5 are “surprising” wrt the query node 1; while the nodes
2, 6-9 are not “surprising” results. Figure 7 present the comparison
between TANGENT and conventional recommendation algorithms
(Rel), where x-axis is the length of the recommendation list and
y-axis is the average surprising nodes in the returned recommendation list. It can be seen that TANGENT consistently gives more surprising results. On average, the “Surprising Gain” of TANGENT
on synthetic data sets is 1.95.
4.2 Evaluations on MovieLens Data Set
Here, we present the experimental result on a real movie-rating
data set MovieLens (http://www.movielens.org/). MovieLens data set was collected by GroupLens Research Project at the
University of Minnesota and contains 100,000 rating information
from 943 users on 1682 movies. Each user has rated at least 20
movies from 1 (strongly unsatisfactory) to 5 (strongly satisfactory).
Using this data set, we construct a user-movie bipartite graph.
We choose positive ratings (4 and 5) and connect users and movies
by edges weighted by 4rating−4 in order to emphasize strongly satisfactory ratings. The reason why we do not take into account negative ratings (1 - 3) is that treating negative ratings requires another
mechanism and we would like to focus on the evaluation of effectiveness of TANGENT algorithm. As a result, a user who gives
only negative ratings and movies which receive only negative ratings are neglected; and 942 users, 1447 movies and 55375 ratings
remain. We apply BB Lin [32] to our system for fast computation
of relevance scores and pre-compute only R.
Case Studies. Figure 8 illustrates the transition of rankings between the relevance score and our TANGENT score. For each
movie, we mention its genre(s) - the abbreviations are in the upper right of the figure. The top of Figure 8 are for users who prefer
to slapstick movies. Notice that the top 10 movies by relevance
score consist mainly of comedy movies. On the other hand, niche
comedy movies such as “Ace Ventura: When Nature Calls” and
“Renaissance Man” are out of top 10 ranking by TANGENT score
and popular comedy movies such as “The Princess Bride”, “Toy
Story”, “Monty Python and the Holy Grail” and “Men in Black”
emerge instead. That is, the TANGENT algorithm recommends a
wider variety of genres and gives No.1 rank to “Star Wars”, which
scores high with both user preference as well as with the connectivity to other groups. Note that, especially “The Flintstones” decreases its ranking dramatically, because it has only one positive
rating.
The lists on the bottom of Figure 8 are for users whose preference is horror movies. Although the transition between two lists is
more moderate than that in case of slapstick movies, TANGENT al-
average suprising nodes
average suprising nodes
0.3
1.5
1
0.5
0
1
2
3
4
recommendation list length
5
Figure 9: Comparison of TANGENT and conventional recommendation algorithms on MovieLens data set. Higher is better.
Comparison with Relevance Score. Here, for a query movie q (or
the query user who likes movie q). We say a recommended movie
i is a “surprising movie” if (1) movies i and q share some common genres; and (2) movie i has some new genres that the query
movie q does not have. For example, for the query movie “Robin
Hood: Men in Tights (Comedy)”, “Jack (Comedy and Drama)” is
treated as a surprising recommendation; while neither “Spy Hard
(Comedy)” or “Raiders of the Lost Ark (Action and Adventure)” is
treated as surprising recommendations. Figure 9 presents the comparison between TANGENT and conventional recommendation algorithms (Rel), where x-axis is the length of the recommendation
list and y-axis is the average surprising nodes in the returned recommendation list. Again, TANGENT consistently gives more surprising results and the “Surprising Gain” of TANGENT on this data
set is 0.08.
4.3 Evaluations on CIKM Data Set
This data set is from CIKM proceedings (http://www.informatik.
uni-trier.de/ ley/db /conf/cikm/). We construct an author-paper bipartite graph. The authors are annotated with one or more keywords as his/her attribute based on the session names where the
corresponding paper was presented. For instance, “Tali Brodianskiy” has published a paper (titled with “Self-Correcting Queries
for XML”) in CIKM 2007 and the paper was presented in “XML
Query Processing” session. Therefore, he is associated with “XML”
and “Query” as his attribute. Totally, we have 952 paper nodes,
1,895 author nodes, and 158 keywords.
Case Studies. Table 2 lists the top-5 recommended authors for
“Frank Hing-Wah Luk” by TANGENT score and by relevance score,
respectively. “Frank Hing-Wah Luk” has published one paper (titled with “Triple-Node Hierarchies for Object-Oriented Dababases
Indexing”) and he is associated with “Index” as his attribute. So,
clearly, he is a databases person in CIKM community. From Table 2, it can be seen that while the two methods agree on the first
two recommended authors (“Ada Wai-Chee Fu” and “Ke Wang”),
TANGENT provides more diverse recommendations compared with
relevance score, - the recommended authors by TANGENT (“Yabo
Xu”, “Jiawei Han”, and “Jian Pei”) are cross-disciplinarity in both
dababases and data mining. On the other hand, relevance score will
recommend pure databases persons (“Weixiong Rao”, “Lei Chen”,
and “Yingyi Bu”) instead.
Comparison with Relevance Score. For a given query author q,
we say the recommended author i is “surprising” if (1) authors q
and i share some common keywords, and (2) the author i has some
new keywords that the query author q does not have. Figure 10
presents the comparison between TANGENT and conventional rec-
Figure 8: Ranked lists by relevance score and one by TANGENT score for user who likes slapstick movies (top) and those who
likes horror movies (bottom). Arrows highlight the transition of ranking. Nomenclature for genre is shown in the upper right
(“Com”:Comedy, and “Hor”:Horror are in bold) TANGENT gives much higher diversity of genres, as desired.
Rank
1
2
3
4
5
by TANGENT
Ada Wai-Chee Fu
Ke Wang
Yabo Xu
Jiawei Han
Jian Pei
Attribute of Authors
Index, Performance, Stream
DB, Mine, Cluster, Pattern, Stream
DB, Mine, Stream
DB, Mine
Mine, Pattern, Forecast, Stream
by Relevance
Ada Wai-Chee Fu
Ke Wang
Weixiong Rao
Lei Chen
Yingyi Bu
Attribute of Authors
Index, Performance Stream
DB, Mine, Cluster, Pattern, Stream
Performance
Performance
Performance
Table 2: Ranked lists by relevance score and by TANGENT score for query author “Frank Hing-Wah Luk” on CIKM data set.
“Frank Hing-Wah Luk” has published 1 paper in CIKM titled with “Triple-Node Hierarchies for Object-Oriented Dababases Indexing” and he is associated with “Index” as his attribute.
ommendation algorithms (Rel), where x-axis is the length of the
recommendation list and y-axis is the average surprising nodes in
the returned recommendation list. Again, TANGENT consistently
gives more surprising results and the “Surprising Gain” of TANGENT on this data set is 0.22.
0.78; while on the bipartite graph constructed from “KDD” and
“SIGGRAPH”, TANGENT achieves 0.70 “Surprising Gain” etc.
1.5
SIGMOD
ICML
TANGENT
Rel
CIKM
average suprising nodes
1.8
TANGENT
Rel
1.6
average suprising nodes
1.4
1.2
1
WWW
SIGIR
0.5
1
ISMB
0.8
SIGGRAPH
SIGCOMM
0.6
0
0.4
0.78
0.50
0.61
0.32
0.51
0.69
recommendation list length
0.70
0.39
0.2
0
1
2
3
4
recommendation list length
5
Figure 10: Comparison of TANGENT and conventional recommendation algorithms on CIKM data set. Higher is better.
4.4 Evaluations on DBLP Data Set
Case Studies. We also test the proposed TANGENT on DBLP
data set (http://www.informatik.uni-trier.de/ ley/db/). Here, we construct a series of different author-paper bipartite graphs from two
conferences. One conference is always “KDD”, and the other conference is either “SIGMOD”, “ICML”, “WWW”, “SIGIR”, “CIKM”,
“SIGCOMM”, “SIGGRAPH” or “ISMB”. Table 3 gives the 1st recommended authors on such bipartite graphs by TANGENT score
and by relevance score, respectively. We can see that TANGENT
provides more surprising recommendations compared with relevance score. For example, on the bipartite graph from “KDD”
and “ICML”, conventional recommendation algorithms will recommend “Moiss Goldszmidt” for “Lise Getoor”, which makes sense
since both of them are interested in probabilistic reasoning and
graphical models. On the other hand, TANGENT will recommend
“Charu C. Aggarwal” instead. “Charu C. Aggarwal” is mainly interested in performance, data mining and databases. So, compared
with “Moiss Goldszmidt”, “Charu C. Aggarwal” is a more surprising recommendation for “Lise Getoor”. Yet, the recommendation
by TANGENT is still close enough to the query author. For instance, “Charu C. Aggarwal” is also interested in uncertainty in
databases which is closely related to probabilistic reasoning, - one
of the research interest of “Lise Getoor”.
Comparison with Relevance Score. Here, we use the authors who
publish in only one of the two conferences as the query authors.
And if the recommended author publishes in both conferences, we
say that it is a surprising recommendation. Figure 11 presents the
comparison between TANGENT and traditional recommendation
algorithms (Rel), where we always fix the length of the ranked list
to be 5 and the number below the corresponding bars is the “Surprising Gain”. Again, TANGENT consistently gives more surprising results. For example, on the bipartite graph constructed from
“KDD” and “SIGMOD”, the “Surprising Gain” of TANGENT is
Figure 11: Comparison of TANGENT and conventional recommendation algorithms on DBLP data set. Author-Paper bipartite graph is constructed from “KDD” plus one more conference. The number below the corresponding bars is the “Surprising Gain”. Higher is better.
5. CONCLUSIONS
We define a novel recommendation problem, namely, how to
make a recommendation that broadens the horizons of the user,
in the sense that it is close enough to his/her current interests to
be pleasant, but also towards a new area that the user has not discovered yet. The motivation is how to respond to a user that says
“surprise me”: suppose that a user that consistently chooses, say,
slapstick “comedy” movies, may occasionally get bored with that
genre, and s/he would like to try something slightly different - what
should we recommend? As humans, we would probably recommend, say, “horror comedy”, “cartoons”, or a “comedy-musical”.
Our goal is to automate the response to such “surprise me” query.
Our approach is to find items that are close to the user preferences,
while they also have high connectivity to other groups.
One major contribution of this work is exactly the problem definition. Additional contributions are the following:
1. Careful design decisions, so that the resulting method is (a)
parameter-free, (b) effective and (c) fast.
2. Extensive comparison of the numerous alternatives; while all
seem reasonable on paper, several of them suffer from subtle
issues.
3. Experiments on synthetic and real data sets, illustrating the
effectiveness of the proposed method. On the synthetic data
set, our proposed method indeed spots “bridge” nodes. On
the real data set, our method does not follow blindly the user
preferences (as conventional algorithms do), but instead it
makes recommendations that are reasonable and yet off the
beaten path.
Future work could focus on the implementation of TANGENT
on the emerging Hadoop/MapReduce architecture [7], for Tera- and
Peta-byte scale recommender systems.
Querying Author
Soumen Chakrabarti
Andrew Y. Ng
Jiawei Han
Xiaojin Zhu
Pedro Domingos
Lise Getoor
Flip Korn
Christos Faloutsos
Michael I. Jordan
Robert E. Schapire
By TANGENT
Divesh Srivastava
Chengxiang Zhai
Wei-Yin Ma
Naoki Abe
Eamonn J. Keogh
Charu C. Aggarwal
Philip S. Yu
Michael I. Jordan
Christos Faloutsos
Philip S. Yu
By Relevance
William W. Cohen
David M. Blei
Mohammed J. Zaki
Guy Lebanon
Christopher Meek
Moiss Goldszmidt
Michail Vlachos
Ravi Kumar
John D. Lafferty
Leslie P. Kaelbling
Conferences
KDD, SIGMOD
KDD, SIGIR
KDD, SIGIR
KDD, ICML
KDD, ICML
KDD, ICML
KDD, ICML
KDD, ICML
KDD, ICML
KDD, ICML
Table 3: 1st recommended author by relevance score and by TANGENT score on DBLP data set. The co-authors of the query author
are blanked out. The last column shows the conferences that we use to construct the bipartite graphs.
6.
ACKNOWLEDGEMENT
This material is based upon work supported by the National Science Foundation under Grants No. DBI-0640543 IIS-0705359 CNS0721736 IIS0808661. Also, by the iCAST project sponsored by the
National Science Council, Taiwan, under the Grants No. NSC972745-P-001-001 and by the Ministry of Economic Affairs, Taiwan, under the Grants No. 97-EC-17-A-02-R7-0823. Also, under the auspices of the U.S. Department of Energy by University
of California Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344 (LLNL-CONF-404625), subcontracts
B579447, B580840. This work is also partially supported by an
IBM Faculty Award, a Yahoo Research Alliance Gift, a SPRINT
gift, and a gift from Sony, with additional funding from Intel, NTT
and Hewlett-Packard. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, or other funding parties.
7.
REFERENCES
[1] R. Albert, H. Jeong, and A.-L. Barabasi. Diameter of the world wide
web. Nature, (401):130–131, 1999.
[2] L. Backstrom, D. P. Huttenlocher, J. M. Kleinberg, and X. Lan.
Group formation in large social networks: membership, growth, and
evolution. In KDD, pages 44–54, 2006.
[3] R. Bell, Y. Koren, and C. Volinsky. Modeling relationships at
multiple scales to improve accuracy of large recommender systems.
In KDD, pages 95–104, 2007.
[4] M. Bilgic and L. Getoor. Effective label acquisition for collective
classification. In KDD, pages 43–51, 2008.
[5] U. Brandes. A Faster Algorithm for Betweenness Centrality.
Mathematical Sociology, 25(2):163–177, 2001.
[6] A. Broder, R. Kumar, F. Maghoul1, P. Raghavan, S. Rajagopalan,
R. Stata, A. Tomkins, and J. Wiener. Graph structure in the web:
experiments and models. In WWW Conf., 2000.
[7] J. Dean and S. Ghemawat. MapReduce: simplified data processing
on large clusters. Communications of the ACM, 51(1):107–113, 2008.
[8] P. G. Doyle and J. L. Snell. Random Walks and Electric Networks.
Mathematical Association of America, 1984.
[9] F. Fouss, J.-M. Renders, A. Pirotte, and M. Saerens. Random-Walk
Computation of Similarities between Nodes of a Graph with
Application to Collaborative Recommendation. IEEE Transaction on
Knowledge and Data Engineering, 19(3):355–369, 2007.
[10] L. C. Freeman. A Set of Measures of Centrality Based on
Betweenness. Sociometry, 40(1):35–41, March 1977.
[11] D. Gibson, J. Kleinberg, and P. Raghavan. Inferring web
communities from link topology. In Ninth ACM Conference on
Hypertext and Hypermedia, pages 225–234, New York, 1998.
[12] M. Girvan and M. E. J. Newman. Community structure is social and
biological networks.
[13] T. H. Haveliwala. Topic-sensitive PageRank. In WWW, pages
517–526, New York, NY, USA, 2002.
[14] R. Jin, C. Wang, D. Polshakov, S. Parthasarathy, and G. Agrawal.
Discovering frequent topological structures from graph datasets. In
KDD, pages 606–611, 2005.
[15] J. Kamahara, T. Asakawa, S. Shimojo, and H. Miyahara. A
Community-Based Recommendation System to Reveal Unexpected
Interests. In Proceedings of the 11th International Multimedia
Modelling Conference, pages 433–438, Washington, DC, USA, 2005.
[16] G. Karypis and V. Kumar. Multilevel -way hypergraph partitioning.
In DAC, pages 343–348, 1999.
[17] Y. Koren, S. C. North, and C. Volinsky. Measuring and Extracting
Proximity in Networks. In KDD, pages 245–255, 2006.
[18] J. Leskovec, J. M. Kleinberg, and C. Faloutsos. Graphs over time:
densification laws, shrinking diameters and possible explanations. In
KDD, pages 177–187, 2005.
[19] J. Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney.
Statistical properties of community structure in large social and
information networks. In WWW, pages 695–704, 2008.
[20] S. M. McNee, J. Riedl, and J. A. Konstan. Being Accurate is Not
Enough: How Accuracy Metrics have hurt Recommender Systems.
In CHI ’06 extended abstracts on Human factors in computing
systems, pages 1097–1101, 2006.
[21] J. Neville, Ö. Simsek, D. Jensen, J. Komoroske, K. Palmer, and H. G.
Goldberg. Using relational knowledge discovery to prevent securities
fraud. In KDD, pages 449–458, 2005.
[22] M. E. J. Newman. The structure and function of complex networks.
SIAM Review, 45:167–256, 2003.
[23] M. E. J. Newman. A measure of betweenness centrality based on
random walks. Social Networks, 27(1):39–54, January 2005.
[24] C. C. Noble and D. J. Cook. Graph-based anomaly detection. In
KDD, pages 631–636, 2003.
[25] L. Page, S. Brin, R. Motwani, and T. Winograd. The PageRank
Citation Ranking: Bringing Order to the Web. Stanford Digital
Library Technologies Project, SIDL-WP-1999-0120, 1999.
[26] C. R. Palmer and C. Faloutsos. Electricity Based External Similarity
of Categorical Attributes. In PAKDD, pages 486–500, 2003.
[27] J. Pei, A. W.-C. Fu, X. Lin, and H. Wang. Computing Compressed
Multidimensional Skyline Cubes Efficiently. In ICDE, pages 96–105,
2007.
[28] P. Resnick, N. Iacovou, M. Suchak, P. Bergstrom, and J. Riedl.
GroupLens: an open architecture for collaborative filtering of
netnews. In Proceedings of the 1994 ACM conference on Computer
supported cooperative work, pages 175–186, New York, NY, USA,
1994.
[29] B. M. Sarwar, G. Karypis, J. Konstan, and J. Riedl. Recommender
Systems for Large-Scale E-Commerce: Scalable Neighborhood
Formation Using Clustering. In Proceedings of the Fifth International
Conference on Computer and Information Technology, 2002.
[30] J. Sun, H. Qu, D. Chakrabarti, and C. Faloutsos. Relevance Search
and Anomaly Detection in Bipartite Graphs. SIGKDD Explorations
Special Issue on Link Mining, 7(7):48–55, January 2005.
[31] H. Tong and C. Faloutsos. Center-piece subgraphs: problem
definition and fast solutions. In KDD, pages 404–413, 2006.
[32] H. Tong, C. Faloutsos, and J.-Y. Pan. Random walk with restart: fast
solutions and applications. Knowledge and Information:Systems,
14(3):327–346, 2008.
[33] F. Wang, S. Ma, L. Yang, and T. Li. Recommendation on Item
Graphs. In ICDM, pages 1119–1123, 2006.
[34] D. Xin, J. Han, X. Yan, and H. Cheng. Mining compressed
frequent-pattern sets. In VLDB, pages 709–720, 2005.